$\displaystyle\int x^n\,dx$ (where $n
e -1$) equals:

Question

$\displaystyle\int x^n\,dx$ (where $n 
e -1$) equals:

Accepted Answer

C. $\dfrac{x^{n+1}}{n+1} + C$

$\dfrac{d}{dx}\left(\dfrac{x^{n+1}}{n+1}ight) = x^n$ for $n 
e -1$, so by anti-differentiation $\int x^n\,dx = \dfrac{x^{n+1}}{n+1} + C$. The exception $n = -1$ is handled separately as $\int \dfrac{1}{x}\,dx = \log|x| + C$.

Answer

$x^n \log x + C$

Answer

$\dfrac{x^{n-1}}{n-1} + C$

Answer

$n x^{n-1} + C$

$\displaystyle\int x^n\,dx$ (where $n \ne -1$) equals: